{"id":"https://openalex.org/W2588054282","doi":"https://doi.org/10.1090/mcom/3262","title":"Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection","display_name":"Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection","publication_year":2017,"publication_date":"2017-02-15","ids":{"openalex":"https://openalex.org/W2588054282","doi":"https://doi.org/10.1090/mcom/3262","mag":"2588054282"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3262","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3262","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03262-2/S0025-5718-2017-03262-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03262-2/S0025-5718-2017-03262-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076382628","display_name":"Lili Ju","orcid":"https://orcid.org/0000-0002-6520-582X"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lili Ju","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100654885","display_name":"Li Xiao","orcid":"https://orcid.org/0000-0002-3063-0869"},"institutions":[{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Li","raw_affiliation_strings":["Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193, People\u00e2\u0080\u0099s Republic of China","Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, 100193, People's Republic of China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081360062","display_name":"Zhonghua Qiao","orcid":"https://orcid.org/0000-0002-0553-1404"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhonghua Qiao","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115603684","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0003-1520-2433"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People\u00e2\u0080\u0099s Republic of China","Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People's Republic of China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3106,"has_fulltext":true,"cited_by_count":133,"citation_normalized_percentile":{"value":0.9621956,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"87","issue":"312","first_page":"1859","last_page":"1885"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8053866624832153},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5741502046585083},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5337693691253662},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5041624307632446},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4965229630470276},{"id":"https://openalex.org/keywords/temporal-discretization","display_name":"Temporal discretization","score":0.4677208960056305},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40992626547813416}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8053866624832153},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5741502046585083},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5337693691253662},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5041624307632446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4965229630470276},{"id":"https://openalex.org/C2778327290","wikidata":"https://www.wikidata.org/wiki/Q17146496","display_name":"Temporal discretization","level":3,"score":0.4677208960056305},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40992626547813416}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3262","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3262","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03262-2/S0025-5718-2017-03262-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/77874","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/77874","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3262","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3262","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03262-2/S0025-5718-2017-03262-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7699999809265137,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G8294247944","display_name":"Fast and Stable Compact Exponential Time Difference Based Methods for Some Parabolic Equations","funder_award_id":"1521965","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322841","display_name":"Universidade de Macau","ror":"https://ror.org/01r4q9n85"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2588054282.pdf","grobid_xml":"https://content.openalex.org/works/W2588054282.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W429183865","https://openalex.org/W1171950265","https://openalex.org/W1483804921","https://openalex.org/W1490180844","https://openalex.org/W1597278668","https://openalex.org/W1718360928","https://openalex.org/W1992445851","https://openalex.org/W1993406962","https://openalex.org/W2027319740","https://openalex.org/W2029449803","https://openalex.org/W2030350543","https://openalex.org/W2037963783","https://openalex.org/W2043988785","https://openalex.org/W2049165066","https://openalex.org/W2050969603","https://openalex.org/W2063201396","https://openalex.org/W2066869483","https://openalex.org/W2072083976","https://openalex.org/W2076729365","https://openalex.org/W2080928083","https://openalex.org/W2088535056","https://openalex.org/W2094884329","https://openalex.org/W2104346351","https://openalex.org/W2126000573","https://openalex.org/W2128204029","https://openalex.org/W2139227432","https://openalex.org/W2152024595","https://openalex.org/W2167347425","https://openalex.org/W2168653054","https://openalex.org/W2183656116","https://openalex.org/W2184266932","https://openalex.org/W2285496323","https://openalex.org/W2328649268","https://openalex.org/W2507097021","https://openalex.org/W2963533073","https://openalex.org/W4211077197","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W3100954504","https://openalex.org/W2499297376","https://openalex.org/W3022449129","https://openalex.org/W1588317520","https://openalex.org/W2606781077","https://openalex.org/W4386731851","https://openalex.org/W125268981","https://openalex.org/W1519862060","https://openalex.org/W2490289125","https://openalex.org/W2742566711"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5],"class":[6],"of":[7,33,53,64,86,115],"exponential":[8],"time":[9,51],"differencing":[10],"(ETD)":[11],"schemes":[12,71,89],"for":[13,47,105,113],"solving":[14],"the":[15,30,34,54,65,76,84,87,92,102,106,110,116,120,127,131],"epitaxial":[16],"growth":[17,114],"model":[18],"without":[19],"slope":[20],"selection.":[21],"A":[22],"linear":[23],"convex":[24],"splitting":[25],"is":[26],"first":[27,66],"applied":[28],"to":[29],"energy":[31,107],"functional":[32],"model,":[35],"and":[36,40,50,61,67,90,109,119],"then":[37],"Fourier":[38],"collocation":[39],"ETD-based":[41],"multistep":[42],"approximations":[43],"are":[44,72,124],"used":[45],"respectively":[46],"spatial":[48],"discretization":[49],"integration":[52],"corresponding":[55],"gradient":[56],"flow":[57],"equation.":[58],"Energy":[59],"stabilities":[60],"error":[62],"estimates":[63],"second":[68],"order":[69],"ETD":[70],"rigorously":[73],"established":[74],"in":[75,130],"fully":[77],"discrete":[78],"sense.":[79],"We":[80],"also":[81],"numerically":[82],"demonstrate":[83],"accuracy":[85],"proposed":[88],"simulate":[91],"coarsening":[93],"dynamics":[94],"with":[95,126],"small":[96],"diffusion":[97],"coefficients.":[98],"The":[99],"results":[100],"show":[101],"logarithm":[103],"law":[104],"decay":[108],"power":[111],"laws":[112],"surface":[117],"roughness":[118],"mound":[121],"width,":[122],"which":[123],"consistent":[125],"existing":[128],"theories":[129],"literature.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":4}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}